Various interactive evolutionary multiobjective optimization methods have been proposed in the literature for problems with multiple, conflicting objective functions. In these methods, a decision maker, who is a domain expert, iteratively provides preference information to guide the solution process while gaining insight into the problem. To compare interactive evolutionary multiobjective optimization methods, a preference-based hypervolume indicator (PHI) has been proposed to quantify the performance of the methods. PHI was the first indicator designed based on some desirable properties of indicators for interactive evolutionary multiobjective optimization methods. However, it has some shortcomings, such as excluding some potentially interesting solutions and being limited to consider a reference point as a type of preference information. In this paper, a modified indicator called PHI+ is proposed to address the mentioned drawbacks. PHI+ modifies the region of interest in PHI. While PHI is directed at methods where a decision maker provides preference information in the form of a reference point, PHI+ is applicable for methods that utilize desirable ranges of objective function values as preference information. Therefore, PHI+ is the first indicator that can handle preference information provided as desirable ranges when evaluating interactive methods. Experimental results show that PHI+ can also better distinguish differences in the performance of interactive evolutionary multiobjective optimization methods.

Solving real-life data-driven multiobjective optimization problems involves many complicated challenges. These challenges include preprocessing the data, modelling the objective functions, getting a meaningful formulation of the problem, and supporting decision makers to find preferred solutions in the existence of conflicting objective functions. In this paper, we tackle the problem of optimizing the composition of microalloyed steels to get good mechanical properties such as yield strength, percentage elongation, and Charpy energy. We formulate a problem with six objective functions based on data available and support two decision makers in finding a solution that satisfies them both. To enable two decision makers to make meaningful decisions for a problem with many objectives, we create the so-called MultiDM/IOPIS algorithm, which combines multiobjective evolutionary algorithms and scalarization functions from interactive multiobjective optimization methods in novel ways. We use the software framework called DESDEO, an open-source Python framework for interactively solving multiobjective optimization problems, to create the MultiDM/IOPIS algorithm. We provide a detailed account of all the challenges faced while formulating and solving the problem. We discuss and use many strategies to overcome those challenges. Overall, we propose a methodology to solve real-life data-driven problems with multiple objective functions and decision makers. With this methodology, we successfully obtained microalloyed steel compositions with mechanical properties that satisfied both decision makers.

Abstract We introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles.